Sound Probabilistic Safety Bounds for Large Language Models

2026-07-23 · Source: cs.CL updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Cybersecurity & Data Privacy · Depth: Expert, extended

Summary

The paper introduces a novel framework for computing rigorous, sound lower bounds on the probability of Large Language Models (LLMs) generating harmful outputs for a given prompt. This method applies Clopper-Pearson confidence intervals and, as its main technical contribution, proposes an algorithm that prioritizes exploring branches in the autoregressive generation tree more likely to produce harmful outputs by leveraging features in the latent space. This approach efficiently computes useful lower bounds, even when true harm probability is extremely small, and provides samples of harmful responses for fine-tuning. Experiments on models like Microsoft Phi-4, Llama-3.2-3B Instruct, and Llama-3.1-8B Instruct demonstrate its effectiveness, yielding non-trivial lower bounds with only 10^3 generated tokens, unlike traditional Monte Carlo or Clopper-Pearson methods which often return zero.

Key takeaway

For AI Scientists and Machine Learning Engineers evaluating LLM safety, this framework offers a critical advancement beyond empirical estimates. You should consider integrating this method to obtain mathematically rigorous lower bounds on harmful output probabilities, especially for high-stakes applications where rare but severe risks are a concern. This enables more robust safety certification and provides concrete harmful samples for targeted model fine-tuning, improving alignment effectively.

Key insights

A new framework computes rigorous, sound lower bounds for LLM harmfulness by actively guiding generation towards unsafe outputs.

Principles

• Harmful prefixes imply harmful continuations in LLM outputs.
• Partial construction of the generation tree yields rigorous lower bounds.
• Latent space features can steer LLM generation towards specific behaviors.

Method

The method computes a harmfulness feature vector from example responses, then iteratively expands the autoregressive generation tree by prioritizing nodes with the highest fitness score (cosine similarity to harmful direction and sequence probability) to find harmful outputs and sum their probabilities.

In practice

• Identify harmful latent space features within LLMs.
• Generate targeted harmful responses for model fine-tuning.
• Certify LLM safety with non-trivial lower bounds on harm probability.

Topics

• LLM Safety
• Formal Verification
• Probabilistic Bounds
• Autoregressive Generation
• Latent Space Features
• Clopper-Pearson Intervals

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Security Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.CL updates on arXiv.org.